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Think you’re bad at math? There’s a reason for that.
People often say, "I'm just not a math person," but the truth is that no one's brain is hardwired for math.
- "I'm just not a math person." This cliche defense suggests some people don't have an innate ability to succeed at math.
- But math ability is not genetically determined, and this myth only strengthens America's growing math anxiety.
- How do people get so good at math? Practice.
Americans have a love-hate relationship with mathematics. On the one hand, we understand that success in our technology-dependent world requires proficiency in mathematics, and if we don't cultivate this proficiency in students, we may languish behind those who do. On the other hand, we're just bad at it.
Research seems to support this view. The National Assessment of Educational Progress found that, in 2015, just 25 percent of 12th graders performed at or above proficiency in mathematics. Nor are we doing well when compared to other countries. The United States' mathematics performance score (474 mean score) falls below the average for all OECD countries (494). Meanwhile, Japan, China, and Singapore are crushing it (mean scores 539, 540, and 564 respectively).
Is it any wonder that the refrain "I'm not a math person" has become hackneyed? This defense contains a troubling subtext: Some people are born good at math, some aren't, and the speaker is the latter. This is simply untrue.
In a conversation with Richard Dawkins, Neil deGrasse Tyson explains why: "If there's any one subject that the greatest number of people say, 'I was never good at insert a topic,' it's going to be math. So I say to myself, 'If our brain were wired for logical thinking, then math would be everyone's easiest subject, and everything else would be harder.' I'm kind of forced to conclude that our brain is not wired for logic."
Tyson's right. The brain is (mostly) not hardwired for mathematics. But if that's the case, then where did the myth of the math person come from, and how can we correct for it?
How we know math ability isn't genetic
While there is no innate math ability in this brain, there sure is a lot of room for math anxiety.
(Photo from Flickr)
The reason skill in mathematics isn't genetically determined is because math hasn't been around long enough to be written into our genes. As developmental psychologist Steven Pinker writes in How the Mind Works:
On evolutionary grounds it would be surprising if children were mentally equipped for school mathematics. These tools were invented recently in history and only in a few cultures, too late and too local to stamp the human genome. The mothers of these inventions were the recording and trading of farming surpluses in the first agricultural civilizations.
With that said, Pinker notes that we do come pre-equipped with some innate mathematical intuitions. For example, toddlers can choose which picture has fewer dots, children can divide snacks to share, and all cultures have words for numbers (even if that lexicon is limited to one, two, and many.) All feats managed with no formal schooling, and all evolutionary advantageous.
Citing the work of mathematician Saunders Mac Lane, Pinker speculates that these intuitions may have provided the inspiration for contemporary branches of mathematics: grouping, arithmetic, geometry, and so on.
These intuitions are not the same as the highly formal rule systems we start learning in elementary school, though. He explains the distinction as so: Anyone can tell you that cutting through a field is shorter than walking its edges, but it takes a mathematician to point out that "the hypotenuse is equal to the sum of the squares on the other two sides."
While mathematical ability may not be congenital, it is worth noting that general intelligence is. To some degree at least. General intelligence is influenced by both genetic and environmental factors, and it can be challenging to study the complex interplay between the two. Raw intelligence will, naturally, help one acquire math skills, but as we'll see, environmental factors should not be underplayed.
Creating a self-fulfilling prophecy
Professors Miles Kimball and Noah Smith are highly critical of the math people myth, calling it "the most self-destructive idea in America today." Writing for the Atlantic, they argue this pernicious idea originates from a pattern children suss out when they first enter math class.
The pattern goes like this:
Some children come from homes where parents teach them math at an early age, while others are first introduced to math in school. The prepared children do well because they are already familiar with the subject matter. The unprepared children struggle because they are not.
As test and homework scores accumulate, the prepared children begin to recognized their successes. They assume they are "math people," take pride in their achievement, learn to enjoy the subject, and push themselves to work harder.
The unprepared children, however, don't realize that the prepared children had a head start. They assume they weren't born "math people," find the subject frustrating, and don't push themselves, believing achievement will remain out of reach because of some unrecifiable deficiency.
The result is that "people's belief that math ability can't change becomes a self-fulfilling prophecy."
Teachers and parents may also perpetuate the math person myth, even when trying to reduce math anxiety and encourage students that they can succeed.
Consider Dr. Randy Palisoc. He claims that math difficulties lie in our dehumanized approach toward teaching it. He believes that if we show students that math is a language "just like English, Spanish or Chinese" and that it can be used to communicate, they will recognize their natural talents and approach the subject with alacrity.
Mathematician Eddie Woo follows a similar tactic, but he relegates mathematics to a human sense, one akin to sight and touch:
Naturally some people are born with sharper sense than the rest of us; others are born with impairment. As you can see, I drew a short straw in the genetic lottery when it came to my eyesight. Without my glasses everything is a blur. I've wrestled with this sense my entire life, but I would never dream of saying, 'Well, seeing has always been a struggle for me. I guess I'm just not a seeing kind of person.'
Both Ralisoc and Woo propose to reduce abstraction in the teaching of math — make it less hieroglyphics on a blackboard and more an exploration of the student's world. That's an admirable goal. I quote them here only to show how the metaphors teachers and parents may use to encourage unprepared students, in fact, perpetrate the genetic myth.
Woo's argument undercuts his own point. A person born with perfect eyesight will effortlessly read the 20/20 line on an eye chart. But if you are born with poor sight, the eye chart will forever look like a lazy post-impressionist painting. Only corrective lenses, not hard work, can change this fact. He wouldn't say, "I'm just not a seeing kind of person," because it's an odd thing to say. But that doesn't make it any less true.
Similarly, math is not a language as Ralisoc claims. Language is something children master effortlessly because their brains are programmed with what linguists call "universal grammar." Every English-speaking child knows that the sentences are spoken in Subject-Verb-Object format and that you add an s to most words to pluralize them. They manage this incredible feat without any formal schooling.The same cannot be said for their multiplication tables.
Linguist Noam Chomsky disregarded this idea: "To say that mathematics is a language is just a metaphoric use of the notion of language. […] It certainly doesn't have the properties of human language. A human language is a natural phenomenon [while] mathematics is a human creation."
Students know this. They understand that eyesight comes naturally, and while they may not have learned about universal grammar, they have a sense that language acquisition came easily to them. They didn't even have to think about it.
Metaphors such as these, even if presented with encouragement, are wrong and reinforced the belief that being a math person requires being born with an innate gift for the subject.
Practice makes proficient
Only practice and hard work will can translate this math teacher's blackboard for students.
(Photo from Wikimedia)
But if math is not hardwired into us, why do some people become math people while others perpetually flounder? According to Pinker, it's the same reason some of us play Carnegie Hall while others don't. Practice.
"Mastery of mathematics is deeply satisfying," Pinker writes, "but it is a reward for hard work that is not itself always pleasurable. Without the esteem for hard-won mathematical skills that is common in other cultures, the mastery is unlikely to blossom."
To promote this sense of hard work and esteem, Kimball and Smith argue that we need to change the way we teach math and how our culture views intelligence as a whole. Namely, we need to switch from fixed-mindset mathematicians to growth-mindset ones.
Put simply, a growth mindset sees skills and intelligence as something that can be developed. Failure, in this perspective, is a learning experience that allows for a reassessment before the next attempt. A fixed mindset, on the other hand, sees skills and intelligence as something you are more-or-less born with. Failure, here, is simply evidence of one's own inaptitude.
Kimball and Smith cite the work of psychologists Lisa Blackwell, Kali Trzesniewski, and Carol Dweck to support their argument. Dweck, et al., set up an experiment where they taught students that intelligence was "highly malleable" and could be "developed by hard work." The experiment's control group was only taught how memory works.
The students who learned that intelligence was malleable through hard work received higher grades, and those who switched from a fixed-mindset to a growth one showed the most improvement. The control group showed no such improvement.
Kimball and Smith also note that many East Asian countries — the ones currently dominating in math performance scores — utilize the techniques of hard work and a growth mindset as part of their culture.
Quoting an analysis by Richard Nisbett's, they point out that children in Japan go to school 60 more days a year than U.S. students, study more hours a day, and are culturally more accustom to criticism, leading them to be more persistent to correct failures.
"We see our country moving away from a culture of hard work toward a culture of belief in genetic determinism," Kimball and Smith conclude. "In the debate between 'nature vs. nurture,' a critical third element — personal perseverance and effort — seems to have been sidelined. We want to bring it back, and we think that math is the best place to start."
True, practice and a growth mindset won't guarantee a teaching position in Harvard's math department. If that's your goal, you'll need a healthy dose of raw intelligence and luck. But Kimball and Smith's point isn't that we can all become math geniuses.
Instead, by replacing the math person myth with an ethos of hard work and a growth mindset, we can teach children to achieve their personal best. For most students, this will mean reaching at least high school-level proficiency, but even if it doesn't, it will help them see failure as a chance to improve, not a source of debilitating math anxiety.
Maybe we can't all be math people, but we can all learn to love and appreciate the Queen of the Sciences in our lives.
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Astronomers find these five chapters to be a handy way of conceiving the universe's incredibly long lifespan.
- We're in the middle, or thereabouts, of the universe's Stelliferous era.
- If you think there's a lot going on out there now, the first era's drama makes things these days look pretty calm.
- Scientists attempt to understand the past and present by bringing together the last couple of centuries' major schools of thought.
The 5 eras of the universe<p>There are many ways to consider and discuss the past, present, and future of the universe, but one in particular has caught the fancy of many astronomers. First published in 1999 in their book <a href="https://amzn.to/2wFQLiL" target="_blank"><em>The Five Ages of the Universe: Inside the Physics of Eternity</em></a>, <a href="https://en.wikipedia.org/wiki/Fred_Adams" target="_blank">Fred Adams</a> and <a href="https://en.wikipedia.org/wiki/Gregory_P._Laughlin" target="_blank">Gregory Laughlin</a> divided the universe's life story into five eras:</p><ul><li>Primordial era</li><li>Stellferous era</li><li>Degenerate era</li><li>Black Hole Era</li><li>Dark era</li></ul><p>The book was last updated according to current scientific understandings in 2013.</p><p>It's worth noting that not everyone is a subscriber to the book's structure. Popular astrophysics writer <a href="https://www.forbes.com/sites/ethansiegel/#30921c93683e" target="_blank">Ethan C. Siegel</a>, for example, published an article on <a href="https://www.forbes.com/sites/startswithabang/2019/07/26/we-have-already-entered-the-sixth-and-final-era-of-our-universe/#7072d52d4e5d" target="_blank"><em>Medium</em></a> last June called "We Have Already Entered The Sixth And Final Era Of Our Universe." Nonetheless, many astronomers find the quintet a useful way of discuss such an extraordinarily vast amount of time.</p>
The Primordial era<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yMjkwMTEyMi9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYyNjEzMjY1OX0.PRpvAoa99qwsDNprDme9tBWDim6mS7Mjx6IwF60fSN8/img.jpg?width=980" id="db4eb" class="rm-shortcode" data-rm-shortcode-id="0e568b0cc12ed624bb8d7e5ff45882bd" data-rm-shortcode-name="rebelmouse-image" data-width="1440" data-height="1049" />
Image source: Sagittarius Production/Shutterstock<p> This is where the universe begins, though what came before it and where it came from are certainly still up for discussion. It begins at the Big Bang about 13.8 billion years ago. </p><p> For the first little, and we mean <em>very</em> little, bit of time, spacetime and the laws of physics are thought not yet to have existed. That weird, unknowable interval is the <a href="https://www.universeadventure.org/eras/era1-plankepoch.htm" target="_blank">Planck Epoch</a> that lasted for 10<sup>-44</sup> seconds, or 10 million of a trillion of a trillion of a trillionth of a second. Much of what we currently believe about the Planck Epoch eras is theoretical, based largely on a hybrid of general-relativity and quantum theories called quantum gravity. And it's all subject to revision. </p><p> That having been said, within a second after the Big Bang finished Big Banging, inflation began, a sudden ballooning of the universe into 100 trillion trillion times its original size. </p><p> Within minutes, the plasma began cooling, and subatomic particles began to form and stick together. In the 20 minutes after the Big Bang, atoms started forming in the super-hot, fusion-fired universe. Cooling proceeded apace, leaving us with a universe containing mostly 75% hydrogen and 25% helium, similar to that we see in the Sun today. Electrons gobbled up photons, leaving the universe opaque. </p><p> About 380,000 years after the Big Bang, the universe had cooled enough that the first stable atoms capable of surviving began forming. With electrons thus occupied in atoms, photons were released as the background glow that astronomers detect today as cosmic background radiation. </p><p> Inflation is believed to have happened due to the remarkable overall consistency astronomers measure in cosmic background radiation. Astronomer <a href="https://www.youtube.com/watch?v=IGCVTSQw7WU" target="_blank">Phil Plait</a> suggests that inflation was like pulling on a bedsheet, suddenly pulling the universe's energy smooth. The smaller irregularities that survived eventually enlarged, pooling in denser areas of energy that served as seeds for star formation—their gravity pulled in dark matter and matter that eventually coalesced into the first stars. </p>
The Stelliferous era<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yMjkwMTEzNy9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYxMjA0OTcwMn0.GVCCFbBSsPdA1kciHivFfWlegOfKfXUfEtFKEF3otQg/img.jpg?width=980" id="bc650" class="rm-shortcode" data-rm-shortcode-id="c8f86bf160ecdea6b330f818447393cd" data-rm-shortcode-name="rebelmouse-image" data-width="481" data-height="720" />
Image source: Casey Horner/unsplash<p>The era we know, the age of stars, in which most matter existing in the universe takes the form of stars and galaxies during this active period. </p><p>A star is formed when a gas pocket becomes denser and denser until it, and matter nearby, collapse in on itself, producing enough heat to trigger nuclear fusion in its core, the source of most of the universe's energy now. The first stars were immense, eventually exploding as supernovas, forming many more, smaller stars. These coalesced, thanks to gravity, into galaxies.</p><p>One axiom of the Stelliferous era is that the bigger the star, the more quickly it burns through its energy, and then dies, typically in just a couple of million years. Smaller stars that consume energy more slowly stay active longer. In any event, stars — and galaxies — are coming and going all the time in this era, burning out and colliding.</p><p>Scientists predict that our Milky Way galaxy, for example, will crash into and combine with the neighboring Andromeda galaxy in about 4 billion years to form a new one astronomers are calling the Milkomeda galaxy.</p><p>Our solar system may actually survive that merger, amazingly, but don't get too complacent. About a billion years later, the Sun will start running out of hydrogen and begin enlarging into its red giant phase, eventually subsuming Earth and its companions, before shrining down to a white dwarf star.</p>
The Degenerate era<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yMjkwMTE1MS9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYxNTk3NDQyN30.gy4__ALBQrdbdm-byW5gQoaGNvFTuxP5KLYxEMBImNc/img.jpg?width=980" id="77f72" class="rm-shortcode" data-rm-shortcode-id="08bb56ea9fde2cee02d63ed472d79ca3" data-rm-shortcode-name="rebelmouse-image" data-width="1440" data-height="810" />
Image source: Diego Barucco/Shutterstock/Big Think<p>Next up is the Degenerate era, which will begin about 1 quintillion years after the Big Bang, and last until 1 duodecillion after it. This is the period during which the remains of stars we see today will dominate the universe. Were we to look up — we'll assuredly be outta here long before then — we'd see a much darker sky with just a handful of dim pinpoints of light remaining: <a href="https://earthsky.org/space/evaporating-giant-exoplanet-white-dwarf-star" target="_blank">white dwarfs</a>, <a href="https://earthsky.org/space/new-observations-where-stars-end-and-brown-dwarfs-begin" target="_blank">brown dwarfs</a>, and <a href="https://earthsky.org/astronomy-essentials/definition-what-is-a-neutron-star" target="_blank">neutron stars</a>. These"degenerate stars" are much cooler and less light-emitting than what we see up there now. Occasionally, star corpses will pair off into orbital death spirals that result in a brief flash of energy as they collide, and their combined mass may become low-wattage stars that will last for a little while in cosmic-timescale terms. But mostly the skies will be be bereft of light in the visible spectrum.</p><p>During this era, small brown dwarfs will wind up holding most of the available hydrogen, and black holes will grow and grow and grow, fed on stellar remains. With so little hydrogen around for the formation of new stars, the universe will grow duller and duller, colder and colder.</p><p>And then the protons, having been around since the beginning of the universe will start dying off, dissolving matter, leaving behind a universe of subatomic particles, unclaimed radiation…and black holes.</p>
The Black Hole era<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yMjkwMTE2MS9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYzMjE0OTQ2MX0.ifwOQJgU0uItiSRg9z8IxFD9jmfXlfrw6Jc1y-22FuQ/img.jpg?width=980" id="103ea" class="rm-shortcode" data-rm-shortcode-id="f0e6a71dacf95ee780dd7a1eadde288d" data-rm-shortcode-name="rebelmouse-image" data-width="1400" data-height="787" />
Image source: Vadim Sadovski/Shutterstock/Big Think<p> For a considerable length of time, black holes will dominate the universe, pulling in what mass and energy still remain. </p><p> Eventually, though, black holes evaporate, albeit super-slowly, leaking small bits of their contents as they do. Plait estimates that a small black hole 50 times the mass of the sun would take about 10<sup>68</sup> years to dissipate. A massive one? A 1 followed by 92 zeros. </p><p> When a black hole finally drips to its last drop, a small pop of light occurs letting out some of the only remaining energy in the universe. At that point, at 10<sup>92</sup>, the universe will be pretty much history, containing only low-energy, very weak subatomic particles and photons. </p>
The Dark Era<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yMjkwMTE5NC9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTY0Mzg5OTEyMH0.AwiPRGJlGIcQjjSoRLi6V3g5klRYtxQJIpHFgZdZkuo/img.jpg?width=980" id="60c77" class="rm-shortcode" data-rm-shortcode-id="7a857fb7f0d85cf4a248dbb3350a6e1c" data-rm-shortcode-name="rebelmouse-image" data-width="1440" data-height="810" />
Image source: Big Think<p>We can sum this up pretty easily. Lights out. Forever.</p>
Dr. Katie Mack explains what dark energy is and two ways it could one day destroy the universe.
- The universe is expanding faster and faster. Whether this acceleration will end in a Big Rip or will reverse and contract into a Big Crunch is not yet understood, and neither is the invisible force causing that expansion: dark energy.
- Physicist Dr. Katie Mack explains the difference between dark matter, dark energy, and phantom dark energy, and shares what scientists think the mysterious force is, its effect on space, and how, billions of years from now, it could cause peak cosmic destruction.
- The Big Rip seems more probable than a Big Crunch at this point in time, but scientists still have much to learn before they can determine the ultimate fate of the universe. "If we figure out what [dark energy is] doing, if we figure out what it's made of, how it's going to change in the future, then we will have a much better idea for how the universe will end," says Mack.
A unique exoplanet without clouds or haze was found by astrophysicists from Harvard and Smithsonian.
- Astronomers from Harvard and Smithsonian find a very rare "hot Jupiter" exoplanet without clouds or haze.
- Such planets were formed differently from others and offer unique research opportunities.
- Only one other such exoplanet was found previously.
Munazza Alam – a graduate student at the Center for Astrophysics | Harvard & Smithsonian.
Credit: Jackie Faherty